Unit III

Taxes: What Taxes Do

• Taxes create a wedge between the price consumers pay and the price sellers receive.
  
• They are most commonly modeled as a decrease in either supply or demand.
  • In both cases, they cause a transfer of surplus from consumers and producers to the government.
• The size of the tax equals the vertical distance between the supply and demand curves:
  • \(P_b\): price paid by buyers
    
  • \(P_s\): price received by sellers

Taxes: Supply and Demand Representation

Taxes: Modeling Taxes in Supply & Demand

Link here

Taxes: Tax Incidence (Who Bears the Burden?)

• Tax incidence refers to how the burden of a tax is divided between buyers and sellers.
  
• It is measured by how much each side’s price changes relative to the pre-tax equilibrium price.
  
• Tax incidence depends on elasticity:
  • The side of the market that is less elastic (less responsive to price changes) bears more of the tax burden.

Taxes: Visualizing Tax Incidence

Taxes: Visualizing Tax Incidence

Same link as earlier

Taxes: Elasticities and “Who Benefits?”

• Whether “tax cuts help the rich” depends on the relative elasticities of supply and demand.
  • If supply is more elastic than demand, consumers benefit more from a tax cut.
    
  • If demand is more elastic than supply, producers benefit more.

Taxes: Elasticities and “Who Benefits?”

• Tax cuts on medical companies may benefit patients more than firms.
  • Patients bear much of the tax burden because demand for healthcare is highly inelastic — people can’t easily substitute away from treatment.
• Tax cuts on rental properties often benefit landlords more than tenants.
  • Housing supply is relatively inelastic (you can’t quickly “make” new apartments), while renters can adjust over time, allowing landlords to keep most of the benefit through higher profits rather than lower rents.

Taxes: Elasticities and “Who Benefits?”

• Tax cuts on jet fuel often benefit airlines more than passengers.
  • Air travel demand is fairly elastic (people can choose not to fly), while short-run supply is inelastic (planes and routes are fixed). Airlines end up keeping most of the savings.
• Tax incentives for movie studios or sports teams often benefit the firms themselves rather than local workers or fans.
  • Labor supply in these specialized industries is more elastic, so most of the gains accrue to the producers.

Taxes: Efficiency vs. Equity

• A tax on stock transactions (like a capital gains tax or a financial transaction tax) can fall differently depending on the elasticity of capital supply and demand:
  • If investors can easily move their money elsewhere (highly elastic capital supply),
  • then firms and workers ultimately bear more of the tax burden through lower stock prices, reduced investment, and lower wages.

Taxes: Efficiency vs. Equity

• Taxes on goods with elastic demand or supply create larger deadweight loss (DWL) and raise less revenue.
  
• Taxes on inelastic goods (few substitutes) create smaller DWL and raise more revenue.
  • For example: taxes on housing or cigarettes are less distortionary than taxes on fashion items.

Taxes: Efficiency vs. Equity

• However, taxing inelastic goods raises equity concerns:
  • Economics can tell us which taxes are most efficient (positive analysis),
    
  • but not which are fair or just (normative analysis).
    
  • ⇒ The classic Efficiency vs. Equity Tradeoff.

Taxes: DWL vs. Tax Revenue

Same link as earlier

Taxes: (Own-Price) Elasticity

\(e = \dfrac{\% \Delta q}{\% \Delta p} = \dfrac{\frac{q_2 - q_1}{q_1}}{\frac{p_2 - p_1}{p_1}}\)

• “For every 1% change in price, how much does quantity change by?”
  • \(e < 1:\) inelastic (quantity responds less than price)
    
  • \(e > 1\): elastic (quantity responds more than price)
  • \(e \approx 0\): highly inelastic (almost no quantity response)

Taxes: Cross-Price Elasticity

\(e_{xy} = \dfrac{\%\ \Delta Q_x}{\%\ \Delta P_y}\)

• “For every 1% change in the price of good Y, how much does the quantity demanded of good X change?”
  • \(e_{xy} > 0\): substitutes — when the price of Y rises, demand for X increases
    
  • \(e_{xy} < 0\): complements — when the price of Y rises, demand for X decreases
    
  • \(e_{xy} = 0\): unrelated — no relationship between the goods

Taxes: Research

Cotti et al. (2022): > “We estimate the effect of e-cigarette tax rates on e-cigarette prices, e-cigarette sales, and sales of other tobacco products using NielsenIQ Retail Scanner data from 2013 to 2019. We find that 90% of e-cigarette taxes are passed on to consumer retail prices…”

• Question: Which side of the market is more elastic — supply or demand?
  • Answer: Supply.
    • Producers pass along most of the tax to consumers, implying that supply is relatively inelastic compared to demand.

Taxes: Research

Cotti et al. (2022): > “…We then estimate reduced form and instrumental variables regressions to examine the effects of e-cigarette and cigarette taxes and prices on sales. We calculate an e-cigarette own-price elasticity of -2.2 and a particularly large elasticity of demand for flavored e-cigarettes…”

• Question: What does this elasticity tell us about how consumers respond to taxes on e-cigarettes?
  • Answer: Demand is highly elastic.
    • A 1% increase in price leads to about a 2.2% drop in sales — meaning consumers are very responsive to price changes, especially for flavored products.

Taxes: Research

Cotti et al. (2022): > “Further, we document a cigarette own-price elasticity of -0.4 and positive cross-price elasticities of demand between e-cigarettes and cigarettes, suggesting economic substitution.”

• Question: What does a positive cross-price elasticity between e-cigarettes and cigarettes imply?
  • Answer: They are economic substitutes.
    • When e-cigarette prices rise (due to taxes), cigarette consumption increases — showing that consumers substitute toward traditional cigarettes when vaping becomes more expensive.

Subsidies: What Subsidies Do

• Subsies create a wedge between the price consumers pay and the price sellers receive.
• They are most commonly modeled as an increases in either supply or demand.
  • In both cases, they cause a transfer of surplus from the government to consumers and producers.
• The size of the subsidy equals the vertical distance between the supply and demand curves:
  • \(P_b\): price paid by buyers
    
  • \(P_s\): price received by sellers

Subsidies: DWL

• Like taxes, subsidies create deadweight loss (DWL)
  • Instead of discouraging consumption, they encourage it beyond the efficient level

Subsidies: DWL

• By raising the price producers receive while lowering the price consumers pay, subsidies:
  • Distort relative prices, signaling producers to expand output and consumers to overconsume scarce resources
    
  • Undermine comparative advantage, for example: it is inefficient to subsidize college-educated farmers who produce corn in the U.S. Midwest (where land and fertilizer are heavily subsidized) when similar crops could be grown more efficiently in parts of South America with lower opportunity costs and more favorable climates

Subsidies: DWL

Subsidies: DWL vs. Gov. Spending

Link here

Externalities

• Externalities = spillover effects of an activity that influence the well-being of third parties
  • Social Cost = Private Cost + External Cost
    
  • Social Benefit = Private Benefit + External Benefit
• Prices serve as dynamically efficient signals and incentives that maximize societal welfare*
  • Market supply and demand reflect only the private costs and benefits
    
  • …so long as no external costs or benefits are associated with consumption or production

Negative Externalities

• Negative externalities occur when the social cost of a transaction exceeds the private cost
  • In other words, when costs are borne by individuals outside the market
• Examples include:
  • Pollution’s effect on global temperatures when consuming electricity
    
  • Spreading illness by going out in public while sick
    
  • Noise and congestion from transportation choices

Positive Externalities

• Positive externalities occur when the social benefit of a transaction exceeds the private benefit
  • In other words, when benefits extend to individuals outside the market
• Examples include:
  • The creation of technologies like the internet, where inventors capture only a fraction of the total social value
    
  • The aesthetic and ecological value of lavender fields
    
  • Education, which benefits not only the student but also society through higher productivity, civic engagement, and innovation

Externalities

Just a silly video was shown here

“Internalize the Externality”

• A free market will overproduce goods with negative externalities and underproduce goods with positive externalities
  • Deadweight loss (DWL) arises from over- or under-production relative to the socially optimal level
    
• A Pigouvian tax (or subsidy) corrects this inefficiency
  • Taxes (subsidies) equal to the external cost (benefit) shift the market toward the socially optimal level of output and consumption

“Internalize the Externality”

“Internalize the Externality”: Modeling Negative Externalities

Link here

“Internalize the Externality”: Modeling Positive Externalities

Link here

What counts as an externlity?

• What counts as an externality and what doesn’t?
• Theme: Many “harms” are just price effects (pecuniary), not true external costs.

What counts as an externlity?

• Example 1:
  • You buy the last candy bar on the shelf.
  • Did you impose an external cost on others who wanted it? No.
  • This is rivalry in consumption: if I consume a unit, you can’t consume the same unit.
  • Outcome determined by supply & demand and willingness to pay (or arrive first).
  • No third-party harm beyond not getting the item—that’s a normal market outcome.

What counts as an externlity?

• Example 2: Choosing a Tesla over a Ford
  • You buy a Tesla instead of a Ford.
  • External cost on Ford because it lost a sale? No.
  • That’s competition: firms win customers by improving quality or lowering price.
  • Again: standard supply & demand, not an externality.

What counts as an externlity?

• Example 3: Bitcoin & Electricity Prices
  • LLM models use lots of electricity → raises demand for electricity → higher prices.
  • External cost on non-miners via higher bills? Not a technological externality.
  • This is a price (pecuniary) effect: others face a higher market price, but no third party is directly harmed outside of the price mechanism.
  • Bidding up a price (art auctions, hot housing markets, scarce GPUs) isn’t an externality.
  • Higher prices signal scarcity and value; they allocate goods to higher WTP users.

What counts as an externlity? The Key Distinction

• Pecuniary effects: actions change prices faced by others (consumption reallocation).

• Externalities: actions change others’ production/consumption possibilities directly (e.g., damage, health, productivity).

• If Tesla and Ford compete, they also compete for workers.

  • That’s a pecuniary effect (through prices).

• A factory pollutes a river → fishing becomes harder/costlier.

  • This is not just a price change; it directly degrades others’ production possibilities.

Positive Externalities of New Technology

• Profits incentivize innovation — firms develop new technologies to gain a competitive edge.

• However, in some cases, competition can discourage innovation, especially when:

  • Other firms can quickly copy a new idea, or
    
  • The innovation requires large fixed-cost investments that are hard to recoup.

• One policy solution is to extend intellectual property (IP) rights, which grant inventors the exclusive legal right to make, use, or sell their invention for a limited time.

Positive Externalities of New Tech

• When fixed costs are high, subsidies can be extremely expensive

• Often firms care about the rate of return:

  • \(RR = \frac{Revenus}{Costs} - 1\)
  • \(Revenue = Price \times Quantity\)
  • \(Costs = \text{Fixed Costs} + \text{Variable Costs}\)

• Suppose: \(RR_{pfizer} = (\$10 * 100b) / (\$14b + \$9.5 * 100b) - 1 \approx 3.73%\)

Positive Externalities of New Tech: Hypothetical

Public Goods Problems

Public goods are non-excludable and non-rival in consumption.

• Excludable → You can prevent non-payers from using it.
• Rival → One person’s use reduces availability for others.
• Because public goods are non-excludable and non-rival, markets often fail to provide them efficiently, leading to free-rider problems.

Public Goods Problems

Public Goods Problems: Examples

Public Goods Problems: Examples

Sources of Public Goods Problems

Some key sources of public goods problems include:

• Non-excludability encourages free riding — individuals benefit without contributing.
• Non-rivalry makes it inefficient to exclude anyone, even if they don’t pay.

The Tragedy of the Commons

• The Tragedy of the Commons describes the tendency of any non-excludable resource
  to be overused and under-maintained when individuals act in their own self-interest.
  • Each user has an incentive to extract as much value as possible.
    
  • Because no one owns the resource, no one bears full responsibility for its upkeep.
    
  • Examples include traffic congestion, overfishing, and air pollution.

The Tragedy of the Commons

Managing Common Resources

• Example: In the case of tuna, the stock of fish is the common resource — rival but non-excludable (especially in international waters)

• When fish stocks become depleted, governments may impose shorter fishing seasons.

  • At one point, there were only four days per year to fish for king crabs.
    
  • This creates perverse incentives — fishermen invest in larger, faster boats, leading to continued overfishing.

Managing Common Resources

• Example: In the case of tuna, the stock of fish is the common resource — rival but non-excludable (especially in international waters)

• Cultural norms

  • Linked to Nobel laureate Elinor Ostrom, who showed that community norms can sustain common resources.
    
  • Works best in small, self-governing communities where social pressure enforces cooperation.

Managing Common Resources

Link here

Coase Theorem

• Efficient outcomes can occur when:
  • Transaction costs are low
    
  • Property rights are clearly defined
    
• Example:
  • If the town owns the river, the paper factory can pay to pollute.
    
  • If the factory owns the rights, the town can pay for cleaner water.

Managing Common Resources

• Example: The stock of tuna is a common resource — rival but non-excludable (especially in international waters).

• To address overuse, many governments establish Individually Transferable Quotas (ITQs):

  • These create property rights for a specific tonnage of fish.
    
  • Fishermen are incentivized to maintain the long-term value of their quota.
    
  • Encourages sustainable management rather than short-term overfishing.

• Similar idea: Cap-and-Trade systems, which apply the same property-rights principle to pollution permits.

Why Not Just Ban It?

• If pollution is a negative externality, it might seem logical to simply ban it altogether.
  
• However, some level of pollution is an unavoidable byproduct of productive economic activity.
  
• The goal is not zero pollution, but the socially optimal level — where the marginal benefit of production equals the marginal social cost of pollution.
  
• Think of it like speed limits – the optimal speed limit isn’t zero, even though higher speeds increase risk.
  • We balance safety and efficiency — just as we balance environmental protection and economic output.